Author: Vincent Diepeveen
Date: 15:24:24 10/16/02
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On October 16, 2002 at 09:40:21, Jeremiah Penery wrote: Is Schach 3.0, one of the participants in Aegon 1997 a good enough program for you to measure branching factor? It was one of the deepest searching and fastest PC programs in 1997. Want to use that as a 'standard'? Note that it uses nullmove ANd hashtables ANd singular extensions. Good to use it as a standard isn't it? Shall i produce some outputs for you with it at my K6-300 laptop? I can run it for days if you want to... >On October 16, 2002 at 07:31:01, Vincent Diepeveen wrote: > >>On October 15, 2002 at 13:31:07, James Swafford wrote: >> >>There is 2 things >> >> a) theoretic branching factor without nullmove >> >>that's true for the last so many plies of deep blue and >>the theoretic truth. >> >> b) branching factor with hashtable. >> >>You will see that deep blue is somewhere, like all software programs >>in the middle of this. >> >>126 mln nodes a second. And it got like 12 ply with a bit more >>than 3 minutes. >> >>that's like total branching factor = 12th root from >>126 mln * 180 seconds = 6.0 > >If you mean (180*126m)^(1/12), that equals 7.294. > >>So the real overall b.f. which was achieved was 6.0 >> >>that's lower than the theoretic branching factor of sqrt(40^18) > >If a decent program didn't have a lower number than the 'theoretic branching >factor...' I'd be very surprised. > >BUT, if you insist on this number, and you think they only got 12 plies, they >need to search 4096000000 nodes for 12 plies. They can accomplish that in 32.5 >seconds with 126M n/s. 12.2 plies takes 47 seconds. In 180 seconds, they can >do 12.93 plies, in fact. sqrt(40) is a branching factor of 6.32. With a >branching factor of 6, they can reach 13.3 plies in 180 seconds based upon your >formula. > >Are you going to claim now their branching factor was above 7 just so that it >can fit your formula, when you can calculate it directly from the logfiles and >find out it was less even than 6? > >>Reality is that deep blue's b.f. is looking worse than it is because of >>2 things >> a) the incredible overhead from hardware >> b) the huge inefficiency from parallel search, estimations of 10% out of >> the total nodes of 126MLN a second which it got on average is not >> very realistic still IMHO. > >You're completely misinterpreting their data. They give estimation of around >10% total efficiency (8%/12% in tactical/non-tactical positions) on the 480 >processor machine. This means they were getting average speedup of 48 over a >single-processor machine. We can tell this because they compare to numbers on >the 24-processor machine: "For positions with many deep forcing sequences >speedups averaged about 7, for an observed efficiency of about 30%. For quieter >positions, speedups averaged 18, for an observed efficiency of 75%." >As you can see, 7/24 = 29.2%, and 18/24 = 75%. With a total average speedup of >about 48 on the big machine, you can calculate that their serial node rate would >have been a little over 100M (2.2m x 48). Amazingly, this is about the same as >the theoretical peak (1000M) times the same 10% efficiency mentioned. > >In case you want to recalculate the branching factors based on 100m instead of >126m nodes/sec, 6.93^12.2 / 100m is 180.69 seconds. Still way too high of a >branching factor. Using 6, which is still too high, you get a little over 13 >plies at that node rate in 3 minutes.
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